Representations of Jordan triples
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- by Ottmar Loos PDF
- Trans. Amer. Math. Soc. 185 (1973), 199-211 Request permission
Abstract:
Some standard results on representations of quadratic Jordan algebras are extended to Jordan triples. It is shown that the universal envelope of a finite-dimensional Jordan triple is finite-dimensional, and that it is nilpotent if the Jordan triple is radical. A permanence principle and a duality principle are proved which are useful in deriving identities.References
- N. Jacobson, Lectures on quadratic Jordan algebras, Tata Institute of Fundamental Research Lectures on Mathematics, No. 45, Tata Institute of Fundamental Research, Bombay, 1969. MR 0325715
- Ottmar Loos, Lectures on Jordan triples, University of British Columbia, Vancouver, B.C., 1971. MR 0325717 —, On algebraic groups defined by Jordan structures (to appear).
- Kevin McCrimmon, Representations of quadratic Jordan algebras, Trans. Amer. Math. Soc. 153 (1971), 279–305. MR 268240, DOI 10.1090/S0002-9947-1971-0268240-9
- Kurt Meyberg, Lectures on algebras and triple systems, University of Virginia, Charlottesville, Va., 1972. Notes on a course of lectures given during the academic year 1971–1972. MR 0340353
- Kiyosi Yamaguti, On representations of Jordan triple systems, Kumamoto J. Sci. Ser. A 5 (1962), 171–184 (1962). MR 153716
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 185 (1973), 199-211
- MSC: Primary 17C15
- DOI: https://doi.org/10.1090/S0002-9947-1973-0327857-5
- MathSciNet review: 0327857